The present invention relates to an improvement in wave-riding vehicles. In particular, the invention relates to a small wave-riding vehicle, ridden prone or kneeling, that incorporates a pair of hydrofoils extending below the hull and transversely to the longitudinal axis of the hull, and which support the hull and the rider above the water while traversing across the face of a breaking wave.
FIG. 1 illustrates a surfer (1) on a board (2) traveling laterally across the face (3) of a breaking wave as the wave moves into shoal water. Not all waves are suitable for surfing. If the wave breaks faster than the surfer can keep up, the rider will not be able to successfully complete the ride. At intermediate speeds of progression of the breaking crest the skilled rider will commonly incorporate a variety of maneuvers into the ride while still remaining ahead of the curl. Thus the speed potential of the surfboard, in combination with the rider's skill, determines the spectrum of breaking waves that can be successfully ridden to completion. Similarly, the response and maneuverability of a surfboard, and its ability to maintain speed while executing a maneuver, influences the type and number of maneuvers that the surfer is able to execute on those waves.
While the United States Patent Office, defines a “surfboard” (Class 441/65/74) as a “Device comprising an elongated member of a width comparable to the shoulder width of a user adapted to be propelled by a wave and capable of supporting the user.”, the surfing community normally subdivides this class into a number of types according to how they are ridden. Largely because of ergonomic factors, these types can also be arranged in terms of the average lengths of the boards: “longboard” (9 feet or more in length, ridden standing), “shortboard” (shorter than 9 feet, ridden standing), “kneeboard” (ridden kneeling”), and “paipo board” and “bodyboard” (ridden prone). In fact, “paipo” is a Hawaiian word meaning “short” or “small. In the subsequent discussion, I will use the term “surfboard” to refer to a wave-riding board in which the rider is in the standing position. The terms “board” and “craft” will be used for the collective set of board types under the Patent Office classification. A “rider” or “surfer” refers to the person riding any board.
Wave-riding boards are controlled by the rider shifting mass fore-and-aft, and from side-to-side. The ability to quickly shift mass in these two directions depends to a considerable degree on the riding position. Stand-up surfers have the greatest mobility and weight-shifting capability in fore-and-aft direction. But motions in the side-to-side direction are considerably restricted by the relatively short distance between the heel and the toe (since all the forces exerted by the surfer on the board must lie within the area bounded by the heels and toes of the surfers two feet, or the surfer will fall). Conversely, a paipo or bodyboard rider's capability for rapid weight shifts fore-and-aft is considerably more restricted than for a stand-up surfer, but the rider's capability of shifting weight from side-to-side is increased. These differences affect the maneuvers than can be performed among these board types (e.g. “toes on the nose” vs. “el rollos” vs. aerials, etc.), the details of how they are performed, and the design of the craft.
Numerical simulations, calculations, and observations of the hydrodynamics of boards with planing hulls (“conventional boards”) and hydrofoil boards (“foilboards”) supported by one, or more, hydrofoils (“foils”) when traversing across the face of a wave indicate that a well-designed foilboard can have superior speed and maneuvering performance when compared with a state-of-the-art conventional board. Nevertheless only a small number of foilboard designs exist in the prior art: G. Miller (Kuhns and Shor, 1993); U.S. Pat. No. 3,747,138 (Morgan, 1973); U.S. Pat. No. 5,062,378 (Bateman, 1991); Lum (Miyake, 1998); Hamilton, Randle, Lickle, Murphy, and Mack (Mack, 1998; Daniel, 2004); U.S. Pat. Nos. 6,019,059; 5,809,926 (Kelsey, 2000; Kelsey, 1998); Wayland (Norene, 2000). All of these designs have some undesirable design and stability characteristics that may have contributed to the lack of acceptance of this type of craft by the general surfing community.
Since the designs of conventional boards differ among types of boards (and in particular, between surfboards, and paipo and bodyboards), it is not unreasonable to expect that perhaps a similar situation may exist between types of hydrofoil boards. Hence it is worth noting that virtually all the disclosures with regard to hydrofoil craft via the patent process have been oriented toward surfboards (i.e. longer boards with the rider standing), while with only one exception, all the hydrofoil boards of which I'm aware that have been built and ridden have been paipo boards (i.e. boards at the short end of the size spectrum, and with the rider prone). The sole exception is the stand-up hydrofoil board of Hamilton, et. al., and, as will be discussed subsequently, this latter board is also somewhat unique even among stand-up boards in that it requires an exernal source of power to make the transition to flight mode, and to be towed onto the face of a wave.
As illustrated in FIG. 1, the face (3) of a breaking wave presents a unique environment for the operation of a hydrofoil craft since the sea surface is inclined (often steeply), curved (frequently substantially), and temporally changing (sometimes quickly). There are three slopes to the face of a wave that are important in the design and operation of a wave-riding board. The first of these is the slope of the face of the wave (“waveface slope”=tan θW) at the location of the board as measured in a vertical plane orthogonal to the crest of the wave (4). The second is the slope of the wave face in a vertical plane passing through the longitudinal axis of the board (“longitudinal slope”=tan θT). It is this slope that determines the magnitude of the force propelling the board and rider. The third is the slope of the wave face in a plane perpendicular to the path of the board (“transverse slope”=tan θT). This latter slope, in combination with the design of the board, affects (in a generally adverse manner as the slope increases) the hydrodynamic characteristics of a conventional board with a planing hull. It also can adversely affect the hydrodynamic efficiency and the control of a foilboard, and presents unique design problems that appear to largely have been ignored in the prior art.
These three angles are related to each other via the path angle (θP) of the surfer. This is the angle between the path of the surfer over the bottom and a line paralleling the wave crest. Numerically it is equal to the arc-tangent of the component of the speed of the surfer over the bottom in the direction of progression of the crest of the wave (VW) toward shore divided by the component of the speed of the board parallel to the crest (4) of the wave (VC):
                              tan          ⁢                                          ⁢                      θ            P                          =                              V            W                                V            C                                              {        1        }            tan θL=tan θW·sin θP  {2}tan θT=tan θW·cos θP  {3}
If the surfer changes the position of the board on the face of the wave such that the wave face slope is increased, both the propelling force and the transverse slope increase. As the speed of the board increases in response to this increase in the driving force, the transverse slope is increased and the hydrodynamic efficiency of the board decreases. Hence there is generally an optimum location for the surfer to position the board on the face of the wave to achieve maximum speed.
The earliest hydrofoil board of which I'm aware was designed by Gaylord Miller. A number of copies were built and ridden at Scripps Institution of Oceanography as early as the fall of 1960 (Kuhns and Shor, 1993; Hendricks, 1960). It is a hydrofoil paipo board, ridden prone, and consisting of a plywood hull (6), a single foil (7), and a large fin (8) separating the foil from the hull, as illustrated in FIG. 2. The hydrofoil paipo board designs by Lum and Wayland are similar.
FIG. 3 shows the cross-section of this board when it is positioned on the sloping face (3) of a wave (FIG. 1). The view in FIG. 3 is looking along the path of the board and the section is in the plane perpendicular to the trajectory (or “pathline”) of the board. The magnitude of the transverse slope of the wave face at the location of the board has been chosen so that if it were any steeper, either the hull of the board (6) would be in contact the sea surface (9), or the end of the foil (7) would begin to pierce (or “broach”) the sea surface, or both would occur. I define this critical transverse slope angle (θDT) to be the “design transverse slope angle” (10) for the foilboard. Its magnitude is related to the configuration of the board by the equation:
                              tan          ⁢                                          ⁢                      θ            DC                          ≅                              2            ·                          S              HF                                                          W              H                        +                          B              F                                                          {        4        }            where:                SHF=vertical spacing between the hull and the foil        WH=width of the hull        BF=span of the hydrofoil        
Numerical simulations of the hydrodynamics of an improved version of this configuration indicate that for a typical wave and surfer, the design transverse angle must be 24 degrees, or greater, for a foilboard to achieve the same speed as a conventional board. Except for the Hamilton et. al. and Kelsey designs, all the design transverse angles for the prior art range from about 9 degrees (Morgan; Bateman) to 22 degrees (G. Miller). Hence each of these designs will typically function as a “hydrofoil-assisted board” rather than a true hydrofoil board when traversing across the face of a wave. The design transverse angle is undefined for a board incorporating the Kelsey concept as the hydrofoil is intended to assist in the support of the board rather than support the board free of the water.
The potential for increased performance of a foilboard over a conventional board lies in the increased hydrodynamic efficiency of a foil compared with that of a planing hull. However, if the hull of a foilboard comes in contact with the sea surface, part of the load will be transferred from the foil to the hull, and the hydrodynamic efficiency will lie somewhere between that of a foilboard and a planing hull. Similarly, if a portion of the foil penetrates through the sea surface, the lift/drag ratio and wetted area of the foil will be reduced. This can increase the induced drag by forcing the foil to be operated at an increased angle of attack. Unless the friction and form drag of the foil are reduced by an equal or greater amount due to the reduced wetted area, the overall drag will increase and the speed potential of the foilboard will be compromised.
The Hamilton et. al. design is a unusual craft that mates the hydrofoil assembly from a water sports device (Woolley et. al., 1995) with a modified surfboard. It is intended to be ridden on large to giant shoaling and open ocean waves. In order for the standing rider to control the craft, the surfer is securely attached to the board by snowboard-style boots and bindings. Unlike a traditional surfboard, this surfboard requires an external source of power, such as a power boat or kite, to accelerate the board up to sufficient speed so that the foils can support the weight of the rider and board and then pull the board and rider onto the face of the wave to be ridden. The board is inherently unstable in both pitch and roll (i.e. similar to a unicycle) and hence must be balanced by the rider shifting his weight fore and aft, and from side to side.
Pitch instability is a deficiency of all the prior art except, perhaps, for the tandem surface-piercing designs disclosed in U.S. Pat. No. 3,747,138 (Morgan, 1973), or if one or more of the foils are broached. All of these craft depend on the rider to manually control the elevation of the hull above the sea surface (and, equivalently, the depth of the foil below the sea surface) by shifting his weight fore or aft. Typical speeds through the water are on the order of 16 to 33 feet/sec (Paine, 1974). For a hydrofoil board moving through the water at a speed of 20 feet/second, an error of only 1 degree in setting the angle-of-attack (AOA) of the foil will result in the elevation of the hull above the sea surface changing at a rate of about 0.4 feet per second. Hence the rider has very little time (less than 1 second for the prior art, except for the Hamilton et. al. design) to recognize the situation and make the appropriate corrections.
But that applies only when riding on a level sea surface. In order to operate on the face of a wave where the transverse slope angle approaches the design transverse slope angle without hull contact with the sea surface, or the foil broaching, the hull must be maintained at a unique elevation. Hence as the slope of the wave face increases and approaches the design transverse slope, the rider must make corrections for any deviation from this nominal elevation increasingly quickly.
The elevation of the hull will change unless the pitch angle of the craft relative to the sea surface results in an angle-of-attack that produces no accelerations of the board perpendicular to the sea surface. This pitch angle will change as the board is positioned higher or lower on the face of the wave; or as the board moves farther away from, or closer to, the breaking point of the wave; as the shape of the wave changes as it moves over a varying bathymetry; and especially as the rider executes maneuvers. Hence maintaining the hull elevation and avoiding hull contact or the foil broaching is a virtually impossible task for the rider. Personal experience with, and observations of, the G. Miller board in action reveal that the board is typically ridden with the foil broached. The same can be expected with the other prior art—with the Hamilton et. al. board being a notable exception. However, even with the large separation between the hull and the foils present in this latter design (which gives the rider more time to make a correction), it is a demanding and distracting task for the rider, and large amplitude variations in hull elevation are evident in a video of the craft in action (Laird, 2002). Thus some automatic means of assisting the rider in minimizing deviations of the hull elevation from its design height would be a highly desirable characteristic.
A canard configuration is commonly used in the design of small hydrofoil water craft, although not in the prior art of hydrofoil wave-riding boards. This configuration has a rear (“main”) foil that supports two-thirds, or more of the total load, and a forward (“canard”) foil that supports the remaining load. A primary function of the canard foil is often to regulate the elevation of the hull above the surface of the water within design limits. In some designs, it may also function as a rudder.
One of the most common means of achieving “automatic” control of the flight elevation with a canard foil is the use of surface-piercing foils. A typical design consists of two foil segments (11) which are joined together to form a “V”-shaped foil with either positive (FIG. 4A) or negative (FIG. 4B) dihedral. On a level sea surface, the foil will seek a depth where the vertical component of the lift forces generated by the two foil segments combine to match the total load superimposed on the pair. Any deviation from this equilibrium depth results in an increase or decrease in the wetted area, and a corresponding change in the lift force that acts to bring the foil back to the equilibrium depth. Alternative configurations based on the same principal may have the two sloping segments separated laterally to provide even greater roll stability, or the two sloping segments at the ends of a fully submerged foil segment.
All surface-piercing foils of this type introduce new problems if the foil is operated on a sloping sea surface (9). Since the foil segments are inclined, the force (direction and magnitude represented by the lines (12)) generated by each of the foils have both a vertical and horizontal component. On a level sea surface, the horizontal components of the two foil segments are equal and opposite directed, so they cancel each other. However, on a sloping sea surface, as in FIGS. 4A,B, the foil segment (11) on the high side of the slope will be more deeply submerged and have a greater wetted area than the segment on the other side. Hence that segment will generate a greater force than generated by the segment on the low side, and there will be a net lateral force.
This force can be significant. In the situation shown in FIGS. 4A,B (corresponding to a submerged foil area equal to one half the total foil area), the net lateral force will be 27 to 28 percent of the combined weight of the surfer and board. For a 150 pound surfer and board, this corresponds to about 40 lb. of force, and a corresponding torque of about 120 ft-lb. (for a 3 foot moment arm) around the yaw axis that tends to turn the board away from the face of the wave. Since the center-of-mass of the rider and board is above the center-of-effort of the forces generated by the two foils, there can also be a moment about the roll axis that acts to bank the board into the face of the wave. In the case of negative dihedral, the torque and the roll moment are in the opposite direction of those of the foil with positive dihedral.
Hence surface-piercing foils with positive dihedral (e.g. Bateman, 1991) and with negative dihedral (Morgan, 1973) lead to control problems for the rider when the board is operated on a sloping sea surface—and these problems will become even worse if the two foils are spatially separated from each other. These “unbalanced” conditions also become less manageable as the dihedral angle of one of the foil segments approaches the transverse slope angle of the sea surface—especially if the foil area and the speed through the water are such that the wetted area for equilibrium is about one-half the total foil area.
Another problem with conventional surface piercing foils is that the equilibrium depth varies as the square of the speed of the flow past the foil. Hence if there are large changes in speed, such as when maneuvering on a wave, there can be large variations in the equilibrium elevation of the hull from the design value. Thus the suitability of a traditional surface-piercing foil as the canard foil for a hydrofoil board is problematic.
Miller (1994) and Miller et. al. (1995) disclose an alternative approach for controlling the elevation of a hull of a hydrofoil sailboard above the sea surface. In U.S. Pat. No. 5,309,859, Miller discloses the design of a “surface-tracking” foil that takes advantage of the characteristic that a foil loses lift as the foil approaches the sea surface. Most of the change occurs when the foil is within a chord depth of the sea surface. Hence if the foil is small and of moderate or greater aspect ratio, the change in equilibrium depth with changing speed through the water will be small. The primary problem with this approach is that ventilation of the upper surface of the foil must be avoided if significant variations in the lift force generated by the foil are to be avoided. Thus, in combination with the dependence on the change in lift with proximity to the sea surface, the span of the foil must closely parallel the sea surface if ventilation of the foil is to be minimized.
In U.S. Pat. No. 5,471,942, Miller et. al. (1995) disclose another approach also based on the loss of lift as a foil approaches or emerges from the sea surface. In this case, the problems with ventilation are avoided by using a foil with a super-cavitating cross-sectional shape to promote continuous ventilation of the foil. They teach that the span of the foil must parallel that of the sea surface and disclose means to permit the foil (and its supporting strut) to swivel about an axis parallel to the longitudinal axis of the board so as to maintain this condition. The degree of rotation of the foil and its support in the plane defined by this axis is under the control of the rider. Alternatively, they disclose a foil with dihedral that does not require the control of the rider, but limits the bank angle of the board (rolled to windward) to a specific value (i.e. the dihedral angle). A third alternative is a foil in the shape of an arc of a circle. This allows more variability in the roll angle, but with a reduced surface tracking capability.
Both of these approaches suffer the same unbalanced lateral force problems as the surface-piercing foil discussed above when operated on an inclined surface. However, now the force imbalance is increased as there is no opposing second foil segment to partially counterbalance the lateral force generated by the surface tracking foil. Thus, although the surface tracking approach disclosed by Miller (1994) and Miller et. al. (1995) has the desirable property that the equilibrium depth of submergence of the canard foil on the speed through the water can be significantly reduced in comparison with a traditional surface-piercing foil, the lateral force unbalance problem is magnified.
All of the prior art using fully-submerged foils are unstable in roll and depend on the rider to balance the board by shifting weight from side to side unless the foil is broached. Morgan (1973) discloses designs with tandem inverted “V” shaped surface-piercing foils (as represented by FIG. 4B). On a level sea surface, a properly designed surface-piercing foil with positive dihedral can be stable in roll. But surface-piercing foils with negative dihedral are inherently unstable in roll (even more so than are fully-submerged foils). As noted above, this problem is exacerbated in the presence of a sloping sea surface. Hence it is unlikely that the rider will be able to balance these craft unless the board is banked such that the hull makes contact with the sea surface. A single surface-piercing foil with positive dihedral is disclosed in U.S. Pat. No. 5,062,378 (Bateman, 1991) and may be stable in roll. However, because of the small design transverse slope angle (˜9 degrees), even a small amount of roll will put the hull in contact with the sea surface.
In U.S. Pat. No. 5,722,865, Tatum (1998) discloses a human-powered boat characterized by a very narrow hull. The rider sits atop a bicycle-like frame mounted on top of the hull. Hence the craft has a high center of gravity and is quite unstable in roll. He discloses a system with a vertical canard foil located ahead of the center-of-mass of the craft. The foil swivels around a vertical axis and is connected to the handle bars on the bicycle-like frame to provide roll control. Steering is controlled by a conventional vertically hinged rudder located well aft at the stem of the craft. Two small levers on the ends of the handlebar control the rudder. Hence both hands are required to provide both roll and steering control. Since the hull is narrow, and the center-of-mass of the rider is well above the center-of-buoyancy of the hull, the canard must have considerable wetted area to maintain roll control at the slower speeds. However, the presence of this wetted area adds to the surface friction drag of the craft at high speeds.